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Tetrahedron T(g, h, w) = number of rotes of weight g, height h, wayage w.
5

%I #7 Nov 23 2013 19:48:10

%S 1,1,2,1,1,4,2,8,2,8,1,12,12,28,4,16

%N Tetrahedron T(g, h, w) = number of rotes of weight g, height h, wayage w.

%C T(g, h, w) = |{m : A062537(m) = g, A109301(m) = h, A001221(m) = w}|.

%C This is the column that is labeled "r" in the tabulation of A112095.

%C g = h > 0 implies w = 1 and T(j, j, 1) = 2^(j-1) = A000079(j-1).

%H J. Awbrey, <a href="https://oeis.org/wiki/Riffs_and_Rotes">Riffs and Rotes</a>

%e Table T(g, h, w), omitting empty cells, starts out as follows:

%e g\(h,w) | (0,0) (1,1) (2,1) (2,2) (3,1) (3,2) (4,1) (4,2) (5,1)

%e --------+-------------------------------------------------------

%e 0 ` ` ` | ` 1

%e 1 ` ` ` | ` ` ` ` 1

%e 2 ` ` ` | ` ` ` ` ` ` ` 2

%e 3 ` ` ` | ` ` ` ` ` ` ` 1 ` ` 1 ` ` 4

%e 4 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` 8 ` ` 2 ` ` 8

%e 5 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` `12 ` `12 ` `28 ` ` 4 ` `16

%Y Cf. A000079, A001221, A007097, A014221, A050924.

%Y Cf. A061396, A062504, A062537, A062860, A106177.

%Y Cf. A109300, A109301, A111791 to A111800, A112095.

%K nonn,tabf

%O 1,3

%A _Jon Awbrey_, Sep 08 2005, revised Sep 27 2005